Solution of a Pair of Linear Equations in Two VariablesThe solution of a linear equation in two variables ‘x’ and ‘y’ is a pair of values (one for ‘x’ and other for ‘y’) which makes the two sides of the equation equal.There are two methods to solve a pair of linear equations:(i) algebraic method(ii) graphical method.

Algebraic MethodWe have already studied (i) Substitution method and (ii) Elimination method. Here, we will study cross-multiplication method also.Ifform a pair of linear equations, then the following three situations can arise:(i) If , then the system is consistent.(ii) If ,then the system is inconsistent.(iii) If , then the system is dependent and consistent.

Graphical Method of Solution of a Pair of Linear Equations(i) If the graphs of two equations of a system intersect at a point, the system is said to have a unique solution, i.e., the system is consistent.(ii) If the graphs of two equations of a system are two parallel lines, the system is said to have no solution, i.e., the system is inconsistent.(iii) When the graphs of two equations of a system are two coincident lines, the system is said to have infinitely many solutions, i.e., the system is consistent and dependent.

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